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# Swinging balls and a train tragedy

## The article discusses the physics concepts behind Newton's Cradle, including conservation of momentum and how it relates to train accidents. It also highlights the potential for devastating consequences in such accidents and encourages readers to reflect on recent tragedies.

There’s a fascinating little toy that one of my bosses used to have on his desk. Five identical and gleaming steel balls, each suspended from the frame by two thin strands, arranged in a precise row, each touching the next.

Pull ball #1, at one end of the row, away and let it swing back. As soon as it hit its neighbour, ball #5, at the other end of the row, swings away, then back. As soon as it hits ball #4, ball #1 takes off ... and the show goes on for a while. Through it all, balls #2, #3 and #4 remain stationary. Variation: you can pull balls #1 and #2 away and let them swing back. You guessed it, balls #4 and #5 react at the other end. Similarly, pull three balls aside and three react.

You get the idea, I’m sure. The toy is known as Newton’s Cradle, after the legendary Isaac Newton. I don’t think he invented it, but it takes that name because it demonstrates his Third Law of Motion: every action has an equal and opposite reaction. Thus, let one ball hit the others, and one ball flies off at the other end. And so on.

But Newton’s Cradle is arguably an even better, more intuitive demonstration of what’s known in physics as the conservation of momentum. The ball you pull back and let go accelerates towards its collision, building its momentum on the way. That’s because the momentum of an object is the product of its mass and its velocity. So, an accelerating ball has an increasing velocity, and thus, momentum.

But when it hits another ball, it transfers its momentum there. In effect, this momentum flashes one-by-one through the stationary balls and eventually causes the fifth to swing outwards. Since the balls are all identical, the velocity that fifth one attains is the same as the first had on impact. Or in truth, slightly less, because of friction between the balls, and this is why the back-and-forth swinging gets steadily lower, slower and finally stops.

One more point to make here. Suppose the first ball is heavier than the fifth. What happens? Momentum must still be conserved. But since momentum is the product of mass and velocity, the fifth ball, being lighter than the first, swings out at a higher speed than the first.

With me so far? Now, think of two trains involved in an accident. You remember such a happening, I’m sure. The first train, let’s call it Coromandel, is travelling at 100kmph when it smashes into the rear of the second. That second, let’s call it a freight train, is stationary. Let’s say the freight train’s locomotive is touching, but not actually coupled to its first wagon. On impact, the momentum of the Coromandel is its mass multiplied by 100 kmph. That momentum is transferred to the last wagon of the freight train, and thence from wagon to wagon till it reaches the locomotive. The locomotive, being free to roll, moves forward. In fact, given that we can assume it weighs substantially less than the whole of the Coromandel, it will shoot forward at considerably more than 100kmph. The conserved momentum, after all, is the product of mass and velocity.

In reality, the accident doesn’t happen quite like this. Friction on those rails and between stationary coaches is far more significant a factor than with the balls of Newton’s Cradle. So, we will more likely see the locomotive of the Coromandel climb atop the last wagon of the freight train. Or both mangled or thrown off the tracks along with several more coaches from both trains. The conservation of momentum finds expression in all this mayhem.

Yet, the image of the freight’s locomotive shooting forward is a compelling one. It might make you think, what if there were people in that locomotive and what if all the wagons in the freight train, locomotive included, were somehow totally immobilized? Ignore friction and ask this: on impact, where would the Coromandel’s momentum be transferred to?

To those people, that’s where. Human beings all, each of whom weigh considerably less than the Coromandel. Thus, they will be hurled forward at a considerably higher speed than the Coromandel’s 100kmph at impact.

That is, they will accelerate from stationary to that speed in a fraction of a second. Newton’s Second Law of Motion tells us that their mass multiplied by that acceleration is the force they will exert on whatever they hit. So, what might ensue?

Imagine a woman weighing 70 kg accelerating from 0 to 100kmph in one second. She then represents a force of 7 million Newtons (appropriately, the unit of force is a Newton). Suppose she flies head-first through the air and hits a window. For simplicity, let’s assume the top of her head is a square, 6cm by 6cm. When she hits that window, she will do so with a force of nearly 2000 Newtons for every square millimeter of the top of her head. That’s about twice as much as glass is designed to resist. Meaning, she will shatter the window and land somewhere outside.

Think too of the passengers in the Coromandel. Before the accident, they are moving at 100kmph as well. On impact, they obey Newton’s First Law: a body in motion remains in motion unless acted on by a force. So, they will be hurled forward until they hit something and are stopped.

It’s hard to comprehend the carnage inside the Coromandel’s probably crowded coaches, as bodies fly through the air and slam into partitions, bulkheads or the floor. And if it’s like most Indian trains, there are probably passengers standing in the doorways too, enjoying the view and the breeze - I’ve done that countless times. Try to imagine what happens to those people, as they are flung from the train on impact.

And near Balasore last week, all this was compounded by a third train.

So: Go ahead and play a little with your nearest Newton’s Cradle. Get a sense of what Newton’s Laws and conservation of momentum mean. Then think of hitting something, not as those little balls do, but at 100kmph and more.

That’s what happened to hundreds of unsuspecting people near Balasore last week. Take a moment to remember them.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun.